Student Learning Outcomes

• Write proofs pertaining to relations, equivalence relations, partitions, and equivalence classes.
• Write proofs involving one-to-one functions, onto functions, preimage, and inverse image.
• Write proofs pertaining to finite sets, countable sets, and uncountable sets. Apply the Bernstein-Schroder Theorem to prove the equivalence between sets.
• Use the Axiom of Choice to prove statements pertaining to the cardinality of a set. Apply the Axiom of Choice to prove the Comparability Theorem.
• Use the Heine-Borel Theorem to prove statements involving compact sets.
• Math students feel they have the resources necessary for their success.
• Students will feel that mathematics is a beneficial part of their education
• Use techniques such as contradiction and contrapositive to prove statements.
• Perform set operations using union, intersection, complementation, and DeMorgan's Laws.
• Write proofs involving the well-ordering principle and mathematical induction.
• Use the Bolzano-Weierstrass Theorem to prove statements involving accumulation points and limit points.